Finite Group Databasebeta

← #21447046

Subgroups — #21447046

Order 7808.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840340C211yesmaximal, characteristic
2C2×#14519704C211yesmaximal, characteristic, complemented
3C2×#14519703C211yesmaximal, characteristic, complemented
4#16839761C211yesmaximal, characteristic, complemented
5#16839627C211yesmaximal, characteristic, complemented
6#16839530C211yesmaximal, characteristic, complemented
7C61×#417C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10#14519756—21no—
11#14519753—21no—
12#14519751—21no—
13#14519749—22no—
14#14519748—21no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4×Dic61C2211yescharacteristic
17#14519704—22no—
18#14519703—22no—
19#14519700—21no—
20#14519697—21no—
21#14519684—22no—
22C2×#41×C61C2211yescharacteristic
23C2×M16×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25#103×C61—21no—
26#102×C61—21no—
27#41×C61—21no—
28#41×C61—21no—
29#41×C61—21no—
30#41×C61—21no—
31C2×Q8×C61D411yescharacteristic
32C2×D4×C61—21no—
33C2×D4×C61D411yescharacteristic
34C22×C4×C61—21no—
35C22×C4×C61—21no—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—21no—
38C2×C22⋊D61—22no—
39C22×Dic61—21no—
40C22×Dic61D412yes—
41#11758222—21no—
42#11758222—21no—
43#11758222—21no—
44#11758222—21no—
45C2×D244D411yescharacteristic
46C2×C4×D61—21no—
47C2×Dic122D411yescharacteristic
48M16×C61—21no—
49M16×C61—21no—
50C2×C8×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C22⋊Dic61—22no—
54#11758198—22no—
55C4⋊Dic61—21no—
56C4⋊Dic61—21no—
57#11758196—22no—
58C4×Dic61—21no—
59C4×Dic61D412yescomplemented
60#11758194—21no—
61#11758194—21no—
62C2×#92418—21no—
63C23×C61—21no—
64C23×C61C2×D411yescharacteristic
65C22×D61—21no—
66Q8×C61—21no—
67Q8×C61—21no—
68D4×C61—21no—
69D4×C61—21no—
70D4×C61—41no—
71D4×C61—41no—
72C2×C4×C61—21no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61—42no—
76C2×C4×C61—41no—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C2×C4×C61#4111yescharacteristic
82C2×C4×C61#4111yescharacteristic
83C22⋊D61—41no—
84C22⋊D61—41no—
85C22⋊D61—82no—
86C2×Dic61—21no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—42no—
92D244—21no—
93D244—21no—
94C4×D61—41no—
95C4×D61—41no—
96Dic122—21no—
97Dic122—21no—
98C8×C61—41no—
99#92418—41no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61#12011yescharacteristic
106C22×C61#12111yescharacteristic
107C22×C61#12411yescharacteristic
108C2×D61—41no—
109C2×D61—41no—
110C2×D61—41no—
111C4×C61—41no—
112C4×C61—81no—
113C4×C61#12111yescharacteristic
114C4×C61#12111yescharacteristic
115C4×C61#12311yescharacteristic
116C4×C61#12311yescharacteristic
117Dic61—42no—
118Dic61—41no—
119Dic61—42no—
120#2040—611nomaximal, Sylow
121C2×C61—21no—
122C2×C61—21no—
123C2×C61—81no—
124C2×C61#39411yescharacteristic
125C2×C61#45411yescharacteristic
126C2×C61#45511yescharacteristic
127D61—81no—
128#537—611no—
129C2×#104—611no—
130C2×#104—611no—
131#417—611no—
132#417D6111yescharacteristic, complemented
133#382—611no—
134#343—611no—
135C61#204011yescharacteristic, complemented, Sylow
136C2×#41—611no—
137C2×#41C2×D6111yescharacteristic
138C2×M16—611no—
139C2×M16C2×D6111yescharacteristic
140C22⋊Q8—1221no—
141C22⋊Q8—1221no—
142#121—1221no—
143#121—1222no—
144#121—1221no—
145C2×C4⋊C4—611no—
146C2×C4⋊C4C2×D6111yescharacteristic
147C2×C42—611no—
148#104—1222no—
149#104—1222no—
150#103—21no—
151#103—1221no—
152#102—21no—
153#102—1221no—
154#95—1222no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—1221no—
160#41—1221no—
161#41—1221no—
162#41—1221no—
163C2×Q8—611no—
164C2×Q8C22⋊D6111yescharacteristic
165C2×D4—21no—
166C2×D4—611no—
167C2×D4—1222no—
168C2×D4—1221no—
169C2×D4C22⋊D6111yescharacteristic
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—612no—
173C22×C4—1221no—
174C22×C4—1221no—
175C22×C4C22×D6111yescharacteristic
176M16—21no—
177M16—21no—
178M16—1221no—
179M16—1221no—
180C2×C8—21no—
181C2×C8—1221no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—1222no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C22⋊C4—1222no—
188C22⋊C4—1222no—
189C42—612no—
190C42—1221no—
191C23—21no—
192C23—1221no—
193C23D4×D6111yescharacteristic
194Q8—21no—
195Q8—21no—
196Q8—1221no—
197Q8—1221no—
198D4—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—1221no—
203D4—1221no—
204D4—4882no—
205D4—2441no—
206D4—2441no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—1222no—
213C2×C4—1221no—
214C2×C4—1222no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4—2442no—
220C2×C4#1175822211yescharacteristic
221C2×C4#1175822211yescharacteristic
222C2×C4D4×D6111yescharacteristic
223C2×C4D4×D6111yescharacteristic
224C2×C4#1175822411yescharacteristic
225C2×C4C2×C22⋊D6111yescharacteristic
226C8—41no—
227C8—2441no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—2441no—
234C22—2441no—
235C22—2441no—
236C22#1451974511yescharacteristic
237C22#1451975011yescharacteristic
238C22#1451976311yescharacteristic
239C4—41no—
240C4—81no—
241C4—2442no—
242C4—2442no—
243C4—2441no—
244C4#1451974911yescharacteristic
245C4#1451975011yescharacteristic
246C4#1451975911yescharacteristic
247C4#1451976011yescharacteristic
248C2—21no—
249C2—21no—
250C2—81no—
251C2—4881no—
252C2#1683967711yescharacteristic
253C2#1683993311yescharacteristic
254C2#1683993811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#417C2
socleC22×C61#120
hypercenter#417D61
hypocenterC61#2040
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14519704C2semidirect
3. C2×#14519703C2semidirect
4. #16839761C2semidirect
5. #16839627C2semidirect
6. #16839530C2semidirect
7. C61×#417C2semidirect
59. C4×Dic61D4semidirect
132. #417D61semidirect
135. C61#2040semidirect